Reaction cell and operation method thereof

ABSTRACT

A reaction cell is provided with a vessel-like cell main body and a circular piezoelectric/electrostrictive oscillator fixed to an outside of a bottom surface of the cell main body. The cell main body includes a circular bottom plate portion and a circumferential wall portion which rises from a circumferential edge of the bottom plate portion so as to thereby surround the bottom plate portion. The bottom plate portion and the circumferential wall portion are integrally formed from ceramics. A solution accommodation space is formed above the bottom plate portion and is partially enclosed by the circumferential wall portion. The piezoelectric/electrostrictive oscillator is concentrically adhered to the outside of the bottom surface of the cell main body.

BACKGROUND OF THE INVENTION

1. Field of the invention

The present invention relates to a reaction cell and, more specifically,to a reaction cell in which a biochemical reaction, such as an enzymereaction or nucleic acid hybridization, proceeds, and a method of usingthe reaction cell to carry out and observe chemical reactions.

2. Description of the Related Art

Conventionally, detecting a degree of a reaction or identifying acharacteristic of a sample, the nature of which is unknown, is achievedby receiving the sample into a reaction cell and, after the passage of aprescribed reaction length of time, carrying out colorimetric analysesor the like.

Hybridization between complementary nucleic acid strands is an effectivemethod for detecting and identifying genetic materials. Thehybridization reaction is a chemical technique wherein two nucleic-acidstrands having complementary bases, such as the strands formingmolecules of DNA, are bonded to each other to thereby form adouble-stranded material. For performing an analysis of hybridizednucleic acid strands, one of the nucleic acid strands is labeled with,for example, a fluorescent material or tag before hybridization with itscomplementary nucleic acid strand. After hybridization is complete, theamount of labeled material present in the double-stranded material isdetected in order to thereby measure the hybridized amount of materialin the sample. Namely, the hybridization method is used for theestimation of a base sequence of an unknown nucleic acid material bymeans of detecting whether it has hybridized with its complementarycounterpart. Detection of whether an unknown target genetic material ispresent in a sample occurs when a known base sequence of one nucleicacid strand contacts a complementary base sequence from the sample,which results in the two complementary nucleic acid strands beinghybridized. The hybridized nucleic acid strands are then detected andquantified.

There are cases with various kinds of enzyme reactions, not limited tothe above-described nucleic acid hybridization, where merely putting arelevant solution into the reaction cell results in a failure for thereaction to proceed with a high efficiency. For this reason, it isconsidered as being effective to vibrate and agitate the solution withinthe reaction cell by using a vibrator or an ultrasonic oscillator.

SUMMARY OF THE INVENTION

A reaction measuring device, a DNA analyzer, etc. each of which isprovided with the above-described reaction cell, are desired to beminiaturized for the convenience of using it at a medical scene or alaboratory or in the field, etc. In accordance with this, it has alsobeen demanded that the reaction cell itself should be miniaturized andmade finer. In addition, using expensive material such as a DNA sample,reagent, enzyme, etc. in large amount runs counter to reducing the costfor analysis and production. On the other hand, vibration means such asthe above-described vibrator and ultrasonic oscillator has thedifficulty of reducing the size thereof and, therefore, it is alsodifficult to apply that vibration means to the reaction cell that hasbeen made smaller in size or finer in structure.

Also, even if using the above-described vibrator or ultrasonicoscillator for agitating the solution within the reaction cell, theinternal solution becomes likely to get stagnated or come into a laminarflow. In a case where the solution within the reaction cell is in astate of being stagnated or being in a laminar flow, the reaction ratebecomes likely to depend on a diffusion rate, with the result that theeffect of promoting the reaction within the reaction cell using theabove-described vibration means is small. Especially, in a case wherethe amount of the solution is small and the viscosity of the solution isrelatively high, effective agitation becomes further difficult toperform. Further, in a case where the vibrator or the ultrasonicoscillator is employed, there is the inconvenience that cavitationbecomes likely to occur and this damages the biopolymer in the solution.

The present invention has been made in view of the above-describedproblems and an object thereof is to provide a reaction cell which canbe made small in size and which can enhance the agitation efficiency andrealize the control of the reaction, and a method of using that reactioncell.

The reaction cell of the present invention is provided with a cell thathas provided thereon a circumferential wall portion and a bottom portionso as to accommodate a relevant solution therein and with apiezoelectric/electrostrictive oscillator that is fixed to the outsidesurface of the circumferential wall portion, the bottom portion or apart of the bottom portion and that integrally vibrates.

In the reaction cell of the present invention, thepiezoelectric/electrostrictive oscillator oscillates integrally with thecircumferential wall portion or the bottom portion, thereby the solutionis agitated. Therefore, with the device that is very small in size, itis possible to highly efficiently promote the progress of the reaction.Also, by controlling the vibration length of time of thepiezoelectric/electrostrictive oscillator, the interval at which thevibration is performed, etc., it is possible to control the degree ofthe progress of the reaction of the solution, the reaction length oftime, etc.

Preferably, the piezoelectric/electrostrictive oscillator is providedwith electronic means for detection of its electric constant change. Asthe reaction proceeds, properties of the solution such as viscosity varyand, resultantly, the electric constant of thepiezoelectric/electrostrictive oscillator changes. Therefore, byequipping the oscillator with means for detection of this electricconstant, it is possible to determine the state of reaction of thesolution. In this manner, it is possible to dynamically control thereaction of the solution.

Preferably, when Δd represents an amplitude of thepiezoelectric/electrostrictive oscillator and d represents a length inthe vibration direction of the cell, the vibration of thepiezoelectric/electrostrictive oscillator is set in the way of0.000001<Δd/d<0.01. If 0.000001>Δd/d, the effect of the vibration cannotbe exhibited, whereas, if Δd/d>0.01, the solution, especially in thecase of a solution containing a biopolymer, the decompositions otherthan that intended to be made by the vibration, etc. become likely tooccur. By setting the amplitude to be within the above-described range,more preferable promotion of the reaction is realized.

Preferably, the cell is constructed in a way in which the bottom portionof the cell is formed into a plurality of recesses so as to be partialcells and the plurality of partial cells are disposed in the form of amatrix. As a result of this, performing the reaction of the solution atmultiple positions becomes possible and each of the partial cells can beprovided with a piezoelectric/electrostrictive element. Bysimultaneously or individually controlling the operations of thepiezoelectric/electrostrictive oscillators provided on the cells, itbecomes possible to perform the control of the agitation, the control ofthe reaction, the detection of the status, etc. correspondingly in eachpartial cell. The piezoelectric/electrostrictive element can also bedisposed on portions other than those of the bottom portion havingformed therein those partial cells. In this case, the solutionaccommodated in a portion other than those where the partial cells aredisposed can have its reaction controlled independently from thesolution accommodated within the partial cells. Therefore, the degree offreedom for controlling the reaction is increased.

More preferably, a plurality of the piezoelectric/electrostrictiveoscillators are disposed along the circumferential surface or bottomsurface of the reaction cell and they are sequentially vibrated in thecircumferential direction, or the amplitude and timing of that vibrationare independently controlled. In a case where the solution within thereaction cell is not easily uniformly agitated, the vibration of aplurality of the piezoelectric/electrostrictive oscillators promotesuniform agitation.

More preferably, the circumferential wall portion and the bottom portionare constructed in the way of their being made of zirconia andintegrally sintered. In a case where each of them is made of zirconia,the cell can have accommodated the solution therein so as to lessattenuate the vibration of the piezoelectric/electrostrictiveoscillator. In addition, zirconia has small reactability with rawmaterials of the piezoelectric/electrostrictive oscillator and,therefore, the deterioration of the zirconia does not occur, thereby anintegrally formed cell can be realized. Incidentally, in general,zirconia can be sintered with an additive such as yttria so that acrystalline structure thereof can be made up of a mixture of tetragonalcrystal, cubic crystal, and monoclinic crystal and thereby has asufficiently high level of mechanical strength. In this case, the cellmay be formed into a multilayer structure, a portion of which,especially the inside of the cell that contacts a water-solublesolution, has a higher proportion of the cubic crystal with a highercontent of an additive such as yttria. By doing so, in addition to themerit that the mechanical strength of the cell is maintained, theoccurrence of the crystalline metamorphosis of zirconia at the portionin contact with the solution can be prevented. Consequently, it ispossible to realize the reaction cell, the durability of which has beenmore enhanced.

In place of zirconia, the cell may be made from optical transmissiveceramics. In a case where using the optical transmissive ceramics, thestatus of reaction of the solution can be detected by light. Also, thecell may be made into a hybrid structure wherein the circumferentialwall portion is formed using ceramics and the bottom portion is formedusing transparent glass or synthetic resin. Further, the cell may alsobe made into a structure wherein the circumferential wall portion andbottom portion are formed using transparent glass or synthetic resin andthe piezoelectric/electrostrictive oscillator is adhered onto thecircumferential wall or bottom portion. By having the cell integrallysintered with optical transmissive ceramics, thepiezoelectric/electrostrictive oscillator can be sintered and formeddirectly on the cell. Also, by having the cell made up into a structurewherein the circumferential wall portion is made of ceramics and thebottom portion is made of transparent glass or synthetic resin, thefollowing merits are obtained. Namely, peripheral portions of the cellcan stably be produced employing a manufacturing method that is suitablefor mass-production, such as green sheet lamination, sintering, etc. Inaddition, a combined structure with the transparent glass or syntheticresin as the bottom portion which is suitable for immobilizingbiopolymer, etc. and detecting the status of the reaction through theuse of a light can be realized. This enables providing a reaction cellthat is inexpensive and has high performance. Also, by having the cellmade up into a structure wherein the piezoelectric/electrostrictiveoscillator is adhered onto the circumferential wall portion or thebottom portion, more options about a selection of the material appliedto the circumferential wall portion or bottom portion are given. As aresult, optimum selection of the material becomes possible from thebiochemical point of view.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a plan view of a reaction cell according to a firstembodiment of the present invention;

FIG. 1B is a sectional view of the reaction cell according to the firstembodiment of the present invention, the section being shown taken alonga line IB-IB of FIG. 1A;

FIG. 2A is a plan view of a reaction cell according to a secondembodiment of the present invention;

FIG. 2B is a sectional view of the reaction cell according to the secondembodiment of the present invention, the section being shown taken alonga line IIB-IIB of FIG. 2A;

FIG. 3A is a plan view of a reaction cell according to a thirdembodiment of the present invention;

FIG. 3B is a sectional view of the reaction cell according to the thirdembodiment of the present invention, the section being shown taken alonga line IIIB-IIIB of FIG. 3A;

FIG. 4A is a plan view of a reaction cell according to a fourthembodiment of the present invention;

FIG. 4B is a sectional view of the reaction cell according to the fourthembodiment of the present invention, the section being shown taken alonga line IVB-IVB of FIG. 4A;

FIG. 5A is a plan view of a reaction cell according to a fifthembodiment of the present invention;

FIG. 5B is a sectional view of the reaction cell according to the fifthembodiment of the present invention, the section being shown taken alonga line VB-VB of FIG. 5A;

FIG. 6A is a plan view of a reaction cell according to a sixthembodiment of the present invention;

FIG. 6B is a sectional view of the reaction cell according to the sixthembodiment of the present invention, the section being shown taken alonga line VIB-VIB of FIG. 6A;

FIG. 7A is a plan view of a reaction cell according to a seventhembodiment of the present invention;

FIG. 7B is a sectional view of the reaction cell according to theseventh embodiment of the present invention, the section being showntaken along a line VIIB-VIIB of FIG. 7A;

FIG. 8A is a plan view of a reaction cell according to an eighthembodiment of the present invention;

FIG. 8B is a sectional view of the reaction cell according to the eighthembodiment of the present invention, the section being shown taken alonga line VIIIB-VIIIB of FIG. 8A;

FIG. 9A is a plan view of a reaction cell according to a ninthembodiment of the present invention;

FIG. 9B is a sectional view of the reaction cell according to the ninthembodiment of the present invention, the section being shown taken alonga line IXB-IXB of FIG. 9A;

FIG. 10A is a plan view of a reaction cell according to a tenthembodiment of the present invention;

FIG. 10B is a sectional view of the reaction cell according to the tenthembodiment of the present invention, the section being shown taken alonga line XB-XB of FIG. 10A;

FIG. 11A is a plan view of a reaction cell according to an eleventhembodiment of the present invention;

FIG. 11B is a sectional view of the reaction cell according to theeleventh embodiment of the present invention, the section being showntaken along a line XIB-XIB of FIG. 11A;

FIG. 12A is a plan view of a reaction cell according to a twelfthembodiment of the present invention;

FIG. 12B is a sectional view of the reaction cell according to thetwelfth embodiment of the present invention, the section being showntaken along a line XIIB-XIIB of FIG. 12A;

FIG. 13A is a plan view of a reaction cell according to a thirteenthembodiment of the present invention;

FIG. 13B is a sectional view of the reaction cell according to thethirteenth embodiment of the present invention, the section being showntaken along a line XIIIB-XIIIB of FIG. 13A;

FIG. 14A is a plan view of a reaction cell according to a fourteenthembodiment of the present invention;

FIG. 14B is a sectional view of the reaction cell according to thefourteenth embodiment of the present invention, the section being showntaken along a line XIVB-XIVB of FIG. 14A;

FIG. 15 is a plan view illustrating an example of a method of using areaction cell according to the present invention; and

FIG. 16 is a graph illustrating the relationship between the reactionlength of time and the yield of each of the reaction cell provided witha piezoelectric/electrostrictive oscillator according to the presentinvention and an ordinary cell according to the prior art.

DETAILED DESCRIPTION OF THE INVENTION

A reaction cell and a method of using it according to respectiveembodiments illustrated in the drawings will be described hereinafter.

[Reaction Cell]

First Embodiment

A first embodiment of the present invention will be described withreference to FIGS. 1A and 1B.

A reaction cell 1 according to this embodiment comprises a vessel-likecell main body 2 and a circular piezoelectric/electrostrictiveoscillator 3 which is provided on the underside (outside surface) of abottom portion of the cell main body 2. It is to be noted that, althoughdetails of the piezoelectric/electrostrictive oscillator 3 are notillustrated in the drawings, the piezoelectric/electrostrictiveoscillator 3 has a sandwiched structure wherein a dielectric materialmember is sandwiched between an upper electrode and a lower electrode.In the cell main body 2, a circular bottom plate portion 2A and acircumferential wall portion 2B which rises from a circumferential edgeof the bottom plate portion 2A to thereby surround the bottom plateportion 2A are integrally formed using, for example, zirconia. In thereaction cell 1 having that structure, a space which is surrounded bythe circumferential wall portion 2B on the bottom plate portion 2Aconstitutes a solution accommodation space 4. Thepiezoelectric/electrostrictive oscillator 3, as illustrated in FIG. 1A,is disposed and adhered on the underside of the bottom plate portion 2Aconcentrically with the bottom plate portion 2A. The diameter of thepiezoelectric/electrostrictive oscillator 3 is set to be shorter thanthat of the bottom plate portion 2A. Incidentally, the diameter of thesolution accommodation space of the reaction cell 1 can suitably be setto a value falling within a range of from several tens of μm to severaltens of cm according to the kind of the solution or the purpose ofdetection thereof. Especially, when Δd represents the amplitude of thevibration of the piezoelectric/electrostrictive oscillator 3 and drepresents the length as viewed in the vibration direction, preferably,0.000001<Δd/d<0.01. If 0.000001>Δd/d, the effect of the vibration cannotbe exhibited, whereas, if Δd/d>0.01, the solution, especially in thecase of its being a solution containing biopolymer, the decompositionsother than that intended to be made by the vibration, etc. become likelyto occur.

In the reaction cell 1 according to this embodiment, thepiezoelectric/electrostrictive oscillator 3 is driven in a state where asolution is accommodated within the solution accommodation space 4. Bydoing so, the bottom plate portion 2A makes its deflection oscillation,whereby the vibration can be transmitted to the solution within thesolution accommodation space 4. Incidentally, in a case where thefrequency of the drive is sufficiently higher than the resonancefrequency of the reaction cell 1 having accommodated therein thesolution, or in a case where the rigidity of the bottom plate portion 2Ais sufficiently high, the oscillation which has occurred from thepiezoelectric/electrostrictive oscillator 3 is transmitted to thesolution within the solution accommodation space 4 via the bottom plateportion 2A. And, it is arranged that, by the oscillation beingtransmitted to the solution, the solution be agitated, whereby aprescribed reaction of solution proceeds. Here, the oscillation of thepiezoelectric/electrostrictive oscillator 3 is fine oscillation, and,therefore, agitation can be done without causing the occurrence ofcavitation in the solution and, for example, without thethree-dimensional structure such as a biopolymer being damaged.

Also, because the piezoelectric/electrostrictive oscillator 3 is used asthe oscillation source, concurrent use of other chemical appliances suchas heating means can easily be made.

Incidentally, the piezoelectric/electrostrictive oscillator 3 isconnected to a drive control circuit via a wiring not illustrated sothat the number of oscillations and the oscillation length of time andso forth may suitably be controlled.

Further, to the piezoelectric/electrostrictive oscillator 3 there isconnected via a wiring (not illustrated) a signal generating/analyzingcircuit. A voltage signal which excites feeble oscillation is appliedthereto and there is detected a change in the electric constant whichfollows that oscillation. By doing so, it is possible to determine thespecific gravity, viscosity, etc. of the solution. The status in whichthe reaction within the reaction cell 1 proceeds is detected as above bymeans of the viscosity and, by doing so, it is possible to automaticallyperform optimum oscillation in correspondence with the status ofprogress of the reaction. Detecting the change in the characteristic ofthe fluid in that way is described in, for example, Japanese PatentApplication Laid-Open No. 8-201265. In this embodiment as well, thecontents therein can be referred to.

Second Embodiment

A second embodiment of the present invention will now be described withreference to FIGS. 2A and 2B.

A reaction cell 10 according to this embodiment comprises a vessel-likecell main body 11 and an annular piezoelectric/electrostrictiveoscillator 12 which is provided on the underside of a bottom portion ofthe cell main body 11.

In the cell main body 11, a circular bottom plate portion 11A and acircumferential wall portion 11B which rises from a circumferential edgeof the bottom plate portion 11A to thereby surround the bottom plateportion 11A are integrally formed using, for example, opticaltransmissive alumina. In the reaction cell 10 having that structure, aspace which is surrounded by the circumferential wall portion 11B on thebottom plate portion 11A constitutes a solution accommodation space 13.Incidentally, the diameter of the solution accommodation space 13 of thereaction cell 10 can suitably be set to a value falling within a rangeof from several tens of μm to several tens of cm according to the kindof the solution or the purpose of detection thereof. In this embodimentas well, for the same reason as stated above, when Δd represents theamplitude of the oscillation of the piezoelectric/electrostrictiveoscillator 12 and d represents the length as viewed in the oscillationdirection, preferably, 0.000001<Δd/d<0.01.

The piezoelectric/electrostrictive oscillator 12, as illustrated in FIG.2A, is disposed and adhered on the underside of the bottom plate portion11A concentrically with the bottom plate portion 11A. The maximumdiameter of the piezoelectric/electrostrictive oscillator 12 is set tobe shorter than that of the bottom plate portion 11A. Since as describedabove the piezoelectric/electrostrictive oscillator 12 is annular, thecentral part of the bottom plate 11A constitutes an area where thepiezoelectric/electrostrictive oscillator 12 does not exist. For thisreason, by setting the thickness of the bottom plate portion 11A to beat a value permitting this portion 11A to have optical transmissivity,or by forming the bottom plate portion 11A using a material having goodoptical transmissivity, monitoring the status of the solution at thecentral part of the bottom plate portion 11A becomes possible bymeasuring the optical transmittance at the central part.

In the reaction cell 10, as well, according to this embodiment, whendriving the piezoelectric/electrostrictive oscillator 12 in a statewhere the solution is accommodated within the solution accommodationspace 13, the bottom plate portion 11A makes its deflection oscillation,and this oscillation is transmitted to the solution within the solutionaccommodation space 13. Or, via the bottom plate portion 11A, theoscillation which has occurred in the piezoelectric/electrostrictiveoscillator 12 can be transmitted to the solution within the solutionaccommodation space 13. And, it is arranged that, by the oscillationbeing transmitted to the solution, the solution be agitated whereby thereaction of the solution is promoted.

Third Embodiment

A third embodiment of the present invention will be described withreference to FIGS. 3A and 3B.

A reaction cell 20 according to this embodiment comprises a vessel-likecell main body 21 and a circular piezoelectric/electrostrictiveoscillator 22 which is provided within the cell main body 21. It is tobe noted that, although the details of thepiezoelectric/electrostrictive oscillator 22 are not illustrated, thepiezoelectric/electrostrictive oscillator 22 has a sandwiched structurewherein a dielectric material member is sandwiched between an upperelectrode and a lower electrode. The cell main body 21 is constructed ofa circular bottom plate portion 21A and a circumferential wall portion21B which rises from a circumferential edge of the bottom plate portion21A to thereby surround the bottom plate portion 21A. And the bottomplate portion 21A and the circumferential wall portion 21B areintegrally formed, the bottom plate portion 21A being formed of, forexample, optical transmissive alumina and the circumferential wallportion 21B being formed of, for example, zirconia. In the reaction cell20 having that structure, a space which is surrounded by thecircumferential wall portion 21B on the bottom plate portion 21Aconstitutes a solution accommodation space 23.

The piezoelectric/electrostrictive oscillator 22, as illustrated in FIG.3A, is disposed and adhered along the inside surface of thecircumferential wall portion 21B in the way of its circumferentiallyextending. Like that, in this embodiment as well, it becomes possible todetect the status of reaction of the internal solution using a light byconstructing the bottom plate portion 21A using a structure, ormaterial, having optical transmissivity. Incidentally, in thisembodiment as well, the diameter of the solution accommodation space 23of the reaction cell 20 can suitably be set according to the kind of thesolution or the purpose of detection thereof.

In the reaction cell 20 according to this embodiment, by driving thepiezoelectric/electrostrictive oscillator 22 in a state where thesolution is accommodated within the solution accommodation space, it ispossible to transmit the oscillation which has occurred in thepiezoelectric/electrostrictive oscillator 22 to the solution within thesolution accommodation space 23 directly, or via the bottom plateportion 21A. And, it is arranged that, by the oscillation beingtransmitted to the solution, the solution be agitated whereby aprescribed reaction of solution is promoted.

Incidentally, the piezoelectric/electrostrictive oscillator 22 isconnected to a drive control circuit via a wiring not illustrated sothat the number of oscillations and the oscillation length of time andso forth may suitably be controlled. And, on the surface of thepiezoelectric/electrostrictive oscillator inside the cell there isapplied over an upper electrode thereof a waterproof coat made of resin,etc. in the way in which the waterproof coat covers the oscillator as awhole.

Fourth Embodiment

A fourth embodiment of the present invention will be described withreference to FIGS. 4A and 4B.

A reaction cell 30 according to this embodiment comprises a vessel-likecell main body 31 and a pair of piezoelectric/electrostrictiveoscillators 32 provided on the underside (outside surface) of the cellmain body 31. The cell main body 31 is constructed of a circular bottomplate portion 33, the thickness of which is relatively great, and acircumferential wall portion 34 which rises from the circumferentialedge of the bottom plate portion 33 and which surrounds the bottom plateportion 33, the both portions 33 and 34 being integrally formed using,for example, zirconia.

In the upper surface of the bottom plate portion 33 there are formed apair of U-shaped recesses 35 which, when viewed from above them, arecircular in the way in which they sandwich the central part of thebottom portion 33. These U-shaped recesses 35 each form a solutionaccommodation small space 36 for accommodating therein a relevantsolution. And, the above-described piezoelectric/electrostrictiveoscillator 32 is disposed and adhered on the central part of theunderside of a relatively thin bottom plate 37 of the correspondingU-shaped recess 35. The reaction cell 30 having such structure has thesolution accommodation small space 36 within each U-shaped recess 35 anda solution accommodation large space 38 which is surrounded by thecircumferential wall portion 34 on the bottom plate portion 33. Theabove-described piezoelectric/electrostrictive oscillator 32 iscircular, the diameter of which is smaller than that of the bottom plate37. Incidentally, the solution accommodation large space 38 in thereaction cell 30 can suitably be set to a value falling within a rangeof from several tens of μm to several tens of cm according to the kindof the solution or the purpose of detection thereof.

The reaction cell 30 according to this embodiment may be used in a statewhere the relevant solution is accommodated within only the solutionaccommodation small space 36 alone, or may be used in a state where thesolution is accommodated within the solution accommodation large space38. And, by driving the piezoelectric/electrostrictive oscillator 32,the oscillation which has occurred in the piezoelectric/electrostrictiveoscillator 32 can be transmitted to the solution within the solutionaccommodation small space 36 and the solution within the solutionaccommodation large space 38. And, because the oscillation istransmitted to the solution, the solution is agitated and a prescribedreaction of the solution is promoted. Incidentally, by individuallyoscillation controlling the solution accommodation small space 36, thereaction of the solution in each small space (cavity) is optimized, withthe result that the reaction within the solution accommodation largespace 38 can also be controlled to a desired status of reaction.

Incidentally, in the reaction cell 30, as well, according to thisembodiment, the piezoelectric/electrostrictive oscillator 32 isconnected to a drive control circuit via a wiring not illustrated sothat the number of oscillations and the oscillation length of time andso forth may suitably be controlled.

Fifth Embodiment

A fifth embodiment of the present invention will be described withreference to FIGS. 5A and 5B.

A reaction cell 40 according to this embodiment comprises a vessel-likecell main body 41 and a pair of piezoelectric/electrostrictiveoscillators 42 provided on the underside (outside surface) of the bottomportion of the cell main body 41. The cell main body 41 is constructedof a circular bottom plate portion 33, the thickness of which isrelatively great, and a circumferential wall portion 44 which rises fromthe circumferential edge of the bottom plate portion 43 and whichsurrounds the bottom plate portion 43, the both portions 43 and 44 beingintegrally formed using, for example, zirconia.

In the upper surface of the bottom plate portion 43 there are formed apair of U-shaped recesses 45 which, when viewed from above them, arecircular in the way in which they sandwich the central part of thebottom portion 43. These U-shaped recesses 45 each form a solutionaccommodation small space 46 for accommodating therein a relevantsolution. And, the above-described piezoelectric/electrostrictiveoscillator 42 is disposed and adhered on the central part of theunderside of a relatively thin bottom plate 47 of the correspondingU-shaped recess 45. The reaction cell 40 having such structure has thesolution accommodation small space 46 within each U-shaped recess 45 anda solution accommodation large space 48 which is surrounded by thecircumferential wall portion 44 on the bottom plate portion 43. Theabove-described piezoelectric/electrostrictive oscillator 42 iscircular, the diameter of which is equal to that of the bottom plate 47.Incidentally, the diameter of the solution accommodation large space 48in the reaction cell 40 can suitably be set to a value falling within arange of from several tens of μm to several tens of cm according to thekind of the solution or the purpose of detection thereof.

The reaction cell 40 according to this embodiment may be used in a statewhere the relevant solution is accommodated within only the solutionaccommodation small space 46 alone, or may be used in a state where thesolution is accommodated within the solution accommodation large space48. And, by driving the piezoelectric/electrostrictive oscillator 42,the oscillation which has occurred in the piezoelectric/electrostrictiveoscillator 42 can be transmitted to the solution within the solutionaccommodation small space 46 and the solution within the solutionaccommodation large space 48. And, because the oscillation istransmitted to the solution, the solution is agitated and a prescribedreaction of the solution is promoted. Incidentally, since thepiezoelectric/electrostrictive oscillator 42 has a diameter that isequal to the diameter of the bottom plate 47, the oscillation within theU-shaped recess 45 can be uniformly transmitted to the solution.

Incidentally, in the reaction cell 40, as well, according to thisembodiment, the piezoelectric/electrostrictive oscillator 42 isconnected to a drive control circuit via a wiring not illustrated sothat the number of oscillations and the oscillation length of time andso forth may suitably be controlled.

Sixth Embodiment

A sixth embodiment of the present invention will be described withreference to FIGS. 6A and 6B.

A reaction cell 50 according to this embodiment comprises a vessel-likecell main body 51 and a pair of annular piezoelectric/electrostrictiveoscillators 52 provided on the underside (outside surface) of the bottomportion of the cell main body 51. The cell main body 51 is constructedof a circular bottom plate portion 53, the thickness of which isrelatively great, and a circumferential wall portion 54 which rises fromthe circumferential edge of the bottom plate portion 53 and whichsurrounds the bottom plate portion 53, the both portions 53 and 54 beingintegrally formed using, for example, zirconia.

In the upper surface of the bottom plate portion 53 there are formed apair of U-shaped recesses 55 which, when viewed from above them, arecircular in the way in which they sandwich the central part of thebottom portion 53 therebetween. These U-shaped recesses 55 each form asolution accommodation small space 56 for accommodating therein arelevant solution. And, the above-describedpiezoelectric/electrostrictive oscillator 52 is disposed and adhered onthe central part of the underside of a thin bottom plate 57 of thecorresponding U-shaped recess 55. The reaction cell 50 having suchstructure has the solution accommodation small space 56 within eachU-shaped recess 55 and a solution accommodation large space 58 which issurrounded by the circumferential wall portion 54 on the bottom plateportion 53. The above-described piezoelectric/electrostrictiveoscillator 52 is annular the maximum diameter of which is equal to thatof the bottom plate 57.

Incidentally, the diameter of the solution accommodation large space 58in the reaction cell 50 can suitably be set to a value falling within arange of from several tens of μm to several tens of cm according to thekind of the solution or the purpose of detection thereof. In thereaction cell 50 according to this embodiment, in order to make greatthe depth of the U-shaped recess 55, the thickness of the bottom plateportion 53 is set to have a great thickness. Also, the thickness of thebottom plate 57 is set to have a small thickness so as to permit a lightto pass therethrough. And, since the piezoelectric/electrostrictiveoscillator 52 does not exist at the central part of the bottom plate 57,it is possible to detect the change in the optical transmittance of thesolution due to the progress of the solution within the U-shaped recess55, or to detect the luminous reaction of the solution. In addition, theportion where the piezoelectric/electrostrictive oscillator 52 isdesigned to have no optical transmissivity. Therefore, in a case wheredetecting the luminous reaction, that construction is advantageous fordecreasing the crosstalk of light which is emitted from each U-shapedrecess 55.

The reaction cell 50 according to this embodiment may also be used in astate where the relevant solution is accommodated within only thesolution accommodation small space 56 alone, or may be used in a statewhere the solution is accommodated within the solution accommodationlarge space 58. And, by driving the piezoelectric/electrostrictiveoscillator 52, the oscillation which has occurred in thepiezoelectric/electrostrictive oscillator 52 can be transmitted to thesolution within the solution accommodation small space 56 and thesolution within the solution accommodation large space 58 via the bottomplate 57. And, because the oscillation is transmitted to the solution,the solution is agitated and a prescribed reaction of the solution ispromoted.

Incidentally, in the reaction cell 50, as well, according to thisembodiment, the piezoelectric/electrostrictive oscillator 52 isconnected to a drive control circuit via a wiring not illustrated sothat the number of oscillations and the oscillation length of time andso forth may suitably be controlled.

Seventh Embodiment

A seventh embodiment of the present invention will be described withreference to FIGS. 7A and 7B.

A reaction cell 60 according to this embodiment comprises a vessel-likecell main body 61 and a pair of annular piezoelectric/electrostrictiveoscillators 62 provided within the cell main body 61. The cell main body61 is constructed of a circular bottom plate portion 63, the thicknessof which is great, and a circumferential wall portion 64 which risesfrom the circumferential edge of the bottom plate portion 63 and whichsurrounds the bottom plate portion 63, the both portions 63 and 64 beingintegrally formed using, for example, zirconia.

In the bottom plate portion 63 there are formed a pair of circular holes65 in the way in which they sandwich the central part of the bottomportion 63 therebetween. These circular holes 65 each have formed alongtheir inner-circumferential wall surfaces the above-describedpiezoelectric/electrostrictive oscillator 62. On the underside of thebottom plate portion 63, over its entire surface, there is integrallyfixedly provided a transparent plate 66 consisting of, for example, atransparent glass. Accordingly, the through-holes of thepiezoelectric/electrostrictive oscillator 62 and the transparent plate66 constitute a solution accommodation small space 67 for accommodatingtherein a relevant solution. Since the bottom portion of the solutionaccommodation small space 67 is formed of the transparent plate 66 inthe reaction cell 60 according to this embodiment, it becomes possibleto grasp the status of reaction of the internal solution by measuringthe optical transmittance and luminous reaction and so forth. Inaddition, since the portion where the thick bottom plate portion 63exists is formed of zirconia having no optical transmissivity and,therefore, in a case where detecting the luminous reaction, thatconstruction is advantageous for decreasing the crosstalk of lightemitted from the solution accommodation small space 67.

The reaction cell 60 having such structure has the solutionaccommodation small space 67 and a solution accommodation large space 68which is surrounded by the circumferential wall portion 64 on the bottomplate portion 63. The diameter of the solution accommodation large space68 in the reaction cell 60 can suitably be set to a value falling withina range of from several tens of μm to several tens of cm according tothe kind of the solution or the purpose of detection thereof.

The reaction cell 60 according to this embodiment may also be used in astate where the relevant solution is accommodated within only thesolution accommodation small space 67 alone, or may be used in a statewhere the solution is accommodated within the solution accommodationlarge space 68. And, by driving the piezoelectric/electrostrictiveoscillator 62, the oscillation which has occurred in thepiezoelectric/electrostrictive oscillator 62 can be transmitted directlyto the solution within the solution accommodation small space 67 and thesolution within the solution accommodation large space 68. And, bybecause the oscillation is transmitted directly to the solution, thesolution is reliably agitated and a prescribed reaction of the solutionis promoted.

Incidentally, in the reaction cell 60, as well, according to thisembodiment, the piezoelectric/electrostrictive oscillator 62 isconnected to a drive control circuit via a wiring not illustrated sothat the number of oscillations and the oscillation length of time andso forth may suitably be controlled.

Eighth Embodiment

An eighth embodiment of the present invention will be described withreference to FIGS. 8A and 8B.

A reaction cell 70 according to this embodiment comprises a vessel-likecell main body 71 and a pair of annular piezoelectric/electrostrictiveoscillators 72 provided on the underside (outside surface) of the bottomportion of the cell main body 71 and an annular secondpiezoelectric/electrostrictive oscillator 78 provided within the cellmain body 71. The cell main body 71 is constructed of a circular bottomplate portion 73, the thickness of which is relatively great, and that,when viewed from above the cell main body, is circular and acircumferential wall portion 74 rises from and surrounds thecircumferential edge of the bottom plate portion 73, the both portions73 and 74 being integrally formed using, for example, zirconia. Thesecond piezoelectric/electrostrictive oscillator 78 is formed in such away that it circumferentially extends along the inner-circumferentialsurface of the circumferential wall portion 74.

In the upper surface of the bottom plate portion 73 there are formed apair of U-shaped recesses 75 which, when viewed from above them, arecircular in the way in which they sandwich the central part of thebottom portion 73 therebetween. These U-shaped recesses 75 each form asolution accommodation small space 76 for accommodating therein arelevant solution. And, the above-describedpiezoelectric/electrostrictive oscillator 72 is disposed and adhered onthe underside of a thin bottom plate 77 of the corresponding U-shapedrecess 75.

The first piezoelectric/electrostrictive oscillator 72 is in the form ofan annulus and has a maximum diameter equal to the diameter of thebottom plate 77.

Incidentally, the diameter of the solution accommodation large space 79in the reaction cell 70 can suitably be set to a value falling within arange of from several tens of μm to several tens of cm according to thekind of the solution or the purpose of detection thereof. In thereaction cell 70 according to this embodiment, in order to make greatthe depth of the U-shaped recess 75, the thickness of the bottom plateportion 73 is set to have a great thickness. Also, the thickness of thebottom plate 77 is set to have a small thickness so as to permit a lightto pass therethrough. And, since the firstpiezoelectric/electrostrictive oscillator 72 does not exist at thecentral part of the bottom plate 77, it is possible to detect the statusof solution within the U-shaped recess 75 by measuring the change in theoptical transmittance of the solution.

The reaction cell 70 according to this embodiment may also be used in astate where the relevant solution is accommodated within only thesolution accommodation small space 76 alone, or may be used in a statewhere the solution is accommodated within the solution accommodationlarge space 79. And, by driving the first piezoelectric/electrostrictiveoscillator 72, the bottom plate 77 makes its deflection oscillationwhereby this oscillation can be transmitted to the solution within thesolution accommodation small space 76. Also, by driving the secondpiezoelectric/electrostrictive oscillator 78, the oscillation can betransmitted directly to the solution within the solution accommodationlarge space 79. And, because the oscillation is transmitted to thesolution, the solution is agitated and a prescribed reaction of thesolution is promoted.

Incidentally, in the reaction cell 70, as well, according to thisembodiment, the first and second piezoelectric/electrostrictiveoscillators 72 and 78 are each connected to a drive control circuit viaa wiring (not illustrated) so that the number of oscillations and theoscillation length of time and so forth may suitably be controlled. And,by adjusting the driving timing, amplitude, etc. of each of the firstand second piezoelectric/electrostrictive oscillator, finer agitation ofthe solution and finer control and promotion of the reaction becomepossible.

Ninth Embodiment

A ninth embodiment of the present invention will be described withreference to FIGS. 9A and 9B.

A reaction cell 80 comprises a vessel-like cell main body 81 and aplurality of first piezoelectric/electrostrictive oscillators 82provided on the underside (outside surface) of the bottom portion of thecell main body 81 and a second annular secondpiezoelectric/electrostrictive oscillator 83 provided within the cellmain body 81. The cell main body 81 is constructed of a circular bottomplate portion 84, the thickness of which is relatively great and whenviewed from above the cell main body, is circular and a circumferentialwall portion 85 rises from and surrounds the circumferential edge of thebottom plate portion 84, the both portions 84 and 85 being integrallyformed using, for example, zirconia. The secondpiezoelectric/electrostrictive oscillator 83 is formed in such a waythat it circumferentially extends along the inner-circumferentialsurface of the circumferential wall portion 85. And, the space which issurrounded by the circumferential wall portion 85 on the bottom plateportion 84 constitutes a solution accommodation space 89.

In the upper surface of the bottom plate portion 84 there are formed atthe central part of the bottom plate portion 84 and in the neighborhoodof it a plurality of U-shaped recesses 86. This plurality of U-shapedrecesses 86, when viewed from above them, are circular and theseU-shaped recesses 86 each form a solution accommodation small space 87for accommodating therein a relevant solution. And, the above-describedfirst piezoelectric/electrostrictive oscillator 82 is disposed andadhered on the underside of a thin bottom plate 88 of the correspondingU-shaped recess 86. Incidentally, the firstpiezoelectric/electrostrictive oscillator 82 is in the form of anannulus and has a maximum diameter substantially equal to the diameterof the bottom plate 88.

Incidentally, the diameter of the solution accommodation large space 89in the reaction cell 80 can suitably be set according to the kind of thesolution or the purpose of detection thereof. In the reaction cell 80according to this embodiment, in order to make great the depth of theU-shaped recess 86, the thickness of the bottom plate portion 84 is setto have a great thickness.

Also, the thickness of the bottom plate 88 is set to have a smallthickness so as to permit a light to pass therethrough. And, since thefirst piezoelectric/electrostrictive oscillator 82 does not exist at thecentral part of the bottom plate 88, it is possible to detect the statusof solution within the U-shaped recess 86 by measuring the opticaltransmittance through the bottom plate 88.

The reaction cell 80 according to this embodiment may also be used in astate where the relevant solution is accommodated within only thesolution accommodation small space 87 alone, or may be used in a statewhere the solution is accommodated within the solution accommodationlarge space 89. And, by driving the first piezoelectric/electrostrictiveoscillator 82, which causes the deflection oscillation of each of theplurality of bottom plates 88, the oscillation can be transmitted to thesolution within the solution accommodation small space 87. Also, bydriving the second piezoelectric/electrostrictive oscillator 83, theoscillation can be transmitted directly to the solution within thesolution accommodation large space 89. And, because the oscillation istransmitted to the solution, the solution is agitated and a prescribedreaction of the solution is promoted.

Incidentally, in the reaction cell 80, as well, according to thisembodiment, the first and second piezoelectric/electrostrictiveoscillators 82 and 83 are each connected to a drive control circuit viaa wiring (not illustrated) so that the number of oscillations and theoscillation length of time and so forth may suitably be controlled.

Tenth Embodiment

A tenth embodiment of the present invention will be described withreference to FIGS. 10A and 10B.

A reaction cell 90 comprises a vessel-like cell main body 91 and aplurality of piezoelectric/electrostrictive oscillators 92 provided onthe underside (outside surface) of the bottom portion of the cell mainbody 91. The cell main body 91 is constructed of a circular bottom plateportion 93, the thickness of which is great and when viewed from abovethe cell main body, is circular and a circumferential wall portion 94rises from and surrounds the circumferential edge of the bottom plateportion 93, the both portions 93 and 94 being integrally formed using,for example, zirconia.

In the upper surface of the bottom plate portion 93 there are formed apair of U-shaped recesses 95 each of which, when viewed from above, iscircular in the way in which they sandwich the central part of thebottom plate portion 93. Each of these U-shaped recesses 95 forms asolution accommodation small space 96 for accommodating therein arelevant solution. And, the space which is surrounded by thecircumferential wall portion 94 on the bottom portion 93 forms asolution accommodation large space 98. Incidentally, the bottom plateportion 93 is set to be relatively thick. As a result of the relativelylarge-depth U-shaped recesses 95 being formed in the bottom plateportion 93, the U-shaped recess 95 includes a small-thickness bottomplate 97. Incidentally, the thickness of the bottom plate 97 is set tobe thin enough to permit a light to pass therethrough.

And, on the thin bottom plate 97 of each U-shaped recess 95, there areintermittently disposed and adhered along the circumferential edge ofthe underside of the bottom plate 97 a plurality ofpiezoelectric/electrostrictive oscillators 92. Incidentally, since thepiezoelectric/electrostrictive oscillator 92 is not disposed at thecentral part of the bottom plate 97, it becomes possible, by passing alight from the central part of the bottom plate 97, to grasp the statusof solution (the status of the reaction) within the U-shaped recess 95through the change in the optical transmittance.

Incidentally, the diameter of the solution accommodation large space 98in the reaction cell 90 can suitably be set according to the kind of thesolution or the purpose of detection thereof. The other construction ofthe reaction cell 90 according to this embodiment is the same as thataccording to the sixth embodiment.

Since the reaction cell 90 according to this embodiment is constructedso that the bottom plate 77 has optical transmissivity, it is possibleto detect the status of solution within the U-shaped recess 95 bymeasuring the optical transmittance.

The reaction cell 90 according to this embodiment may also be used in astate where the relevant solution is accommodated within only thesolution accommodation small space 96 alone, or may be used in a statewhere the solution is accommodated within the solution accommodationlarge space 98. And, by driving the piezoelectric/electrostrictiveoscillator 92 which causes the partial deflection oscillation of thebottom plates 97, the oscillation can be transmitted to the solutionwithin the solution accommodation small space 96 and solutionaccommodation large space 98. And, because the oscillation istransmitted to the solution, the solution is agitated and a prescribedreaction of the solution is promoted.

Especially, in this embodiment, by individually driving thepiezoelectric/electrostrictive oscillator 92, the flow of the solutionwithin the solution accommodation small space 96 becomes able to befreely controlled. In addition, agitating the solution so as for it tohave the form of, for example, a vortex also becomes possible whereby itis possible to enhance the agitating efficiency. Also, optimumoscillation which is in compliance with the status of the reaction canbe performed in every solution accommodation small space 96.

Eleventh Embodiment

An eleventh embodiment of the present invention will be described withreference to FIGS. 11A and 11B.

A reaction cell 100 according to this embodiment comprises a vessel-likecell main body 101 and a plurality of firstpiezoelectric/electrostrictive oscillators 102 provided on the underside(outside surface) of the cell main body 101, and a pair of secondpiezoelectric/electrostrictive oscillators 103 provided within the cellmain body 101 and a plurality of third piezoelectric/electrostrictiveoscillators 104.

The cell main body 101 is constructed of a first circular bottom plateportion 105, the thickness of which is great and when viewed from above,is circular and a circumferential wall portion 106 rises from andsurrounds the circumferential edge of the first bottom plate portion105, the both portions 105 and 106 being integrally formed using, forexample, zirconia.

On the circumferential edge portion of the first bottom plate portion105 there are intermittently disposed and fixed along thecircumferential edge of it the third piezoelectric/electrostrictiveoscillators 104. Also, in the bottom plate portion 105 there are formeda pair of first U-shaped recesses 107 at the positions that sandwich thecentral part of the first bottom plate portion 105. In this firstU-shaped recess 107, there is formed the secondpiezoelectric/electrostrictive oscillator 103 in such a way that itcircumferentially extends along the inner-circumferential surface of therecess 107.

Also, on the bottom of the first U-shaped recess 107, there is formed asecond bottom plate portion 108 and, in the second bottom plate portion108, as illustrated in FIG. 11A, there are formed a plurality of secondU-shaped recesses 109 at the central part and in the neighborhoodthereof.

Further, in the bottom of the second U-shaped recess 109, there isformed a third bottom plate portion 110. On the underside of the thirdbottom plate portion 110, there is fixedly provided the above-describedpiezoelectric/electrostrictive oscillator 102. Incidentally, the firstpiezoelectric/electrostrictive oscillator 102 is in the form of anannulus and has a maximum diameter equal to the diameter of the bottomplate portion 110. Also, since the first piezoelectric/electrostrictiveoscillator 102 has formed at its central part a hole, and, from thishole, the third bottom plate portion 110 is exposed.

And, the space which is surrounded by the circumferential wall portion106 on the first bottom plate portion 105 forms a solution accommodationlarge space 111. Also, the space which is surrounded by the secondpiezoelectric/electrostrictive oscillator 103 on the second bottom plateportion 108 forms a solution accommodation middle space 112. Further,the space which is within the second U-shaped recess 109 on the thirdbottom plate portion 110 forms a solution accommodation small space 113.

Incidentally, the diameter of the first bottom plate portion 105 in thereaction cell 100 is preferably set to be at a value falling within arange of from several mm to several tens of cm. Also, the diameter ofthe second bottom plate portion 108 is preferably set to be at a valuefalling within a range of from several tens of μm to several mm.Further, the diameter of the third bottom plate portion 110 ispreferably set to be at a value falling within a range of from severaltens of μm to several mm.

In the reaction cell 100 according to this embodiment, the thickness ofthe third bottom plate portion 110 is set to have a small thickness soas to permit a light to pass therethrough. And, since the firstpiezoelectric/electrostrictive oscillator 102 does not exist at thecentral part of the third bottom plate portion 110, it is possible todetect the status of solution within the second U-shaped recess 109 bymeasuring the optical transmittance through the bottom plate portion110.

The reaction cell 100 according to this embodiment also enables thereaction of the solution to be performed in a state where the solutionis accommodated within only the solution accommodation small space 113alone, or in a state where the solution is accommodated within thesolution accommodation middle space 112, or in a state where thesolution is accommodated within the solution accommodation large space111.

And, by driving the first piezoelectric/electrostrictive oscillator 102,the oscillation which has occurred in the piezoelectric/electrostrictiveoscillator 102 can be transmitted to the solution within the solutionaccommodation small space 113 via the third bottom plate portion 110.Also, by driving the second piezoelectric/electrostrictive oscillator103, the oscillation can be transmitted to the solution within thesolution accommodation middle space 112. Further, by driving the thirdpiezoelectric/electrostrictive oscillator 104, the oscillation can betransmitted to the solution within the solution accommodation largemiddle space 111. As a result, a prescribed reaction of solution can bepromoted within the reaction cell 100.

Incidentally, in the reaction cell 100, as well, according to thisembodiment, the first, second and third piezoelectric/electrostrictiveoscillators 102, 103, and 104 are each connected to a drive controlcircuit via a wiring (not illustrated) so that the number ofoscillations and the oscillation length of time and so forth maysuitably be controlled. Also, the plurality of thirdpiezoelectric/electrostrictive oscillators 104 may be driven insynchronism with each other and, other than this, may also be driven inthe way their driving timings are sequentially shifted in thecircumferential direction illustrated by an arrow (a) in FIG. 11A. Inthis case, the solution within the solution accommodation large space111 can be made to have a macro rotational flow in the circumferentialdirection. Also, the first to the third piezoelectric/electrostrictiveoscillators 102, 103, and 104 can also be driven in a multistage way forevery solution accommodation space.

Also, in the reaction cell 100, each of the first to thirdpiezoelectric/electrostrictive oscillators 102, 103, and 104 is soarranged that it can detect the change in the viscosity that follows thechange in the status of reaction of the solution within the solutionaccommodation small space 113, solution accommodation middle space 112,or solution accommodation large space 111 that it is located close to orit directly contacts with. Concretely, it is arranged that by detectingthe electric constant following the oscillation of eachpiezoelectric/electrostrictive oscillator, the viscosity of the solutioncan be determined.

Twelfth Embodiment

A twelfth embodiment of the present invention will be described withreference to FIGS. 12A and 12B.

A reaction cell 200 according to this embodiment comprises a vessel-likecell main body 201 and a plurality of firstpiezoelectric/electrostrictive oscillators 202 provided on the underside(outside surface) of the cell main body 201, and a pair of secondpiezoelectric/electrostrictive oscillators 203 provided within the cellmain body 201 and a plurality of third piezoelectric/electrostrictiveoscillators 204.

The cell main body 201 is constructed of a first circular bottom plateportion 205, the thickness of which is great, and which, when viewedfrom above, is circular and a circumferential wall portion 206 risesfrom and surrounds the circumferential edge of the first bottom plateportion 205, the both portions 205 and 206 being integrally formedusing, for example, plastics. Incidentally, the inside surface of thecircumferential wall portion 206 is formed into a tapered surface 206Awhich is inclined slantwise inward and downward. On the upper portion ofthe tapered surface 206A of the circumferential wall portion 206 thereis formed the above-described third piezoelectric/electrostrictiveoscillator 204 in such a way that it circumferentially extends along thetapered surface 206A.

Also, in the bottom plate portion 205 there are formed a pair of firstU-shaped recesses 207 at the positions that sandwich the central part ofthe first bottom plate portion 205. In this first U-shaped recess 207,there is formed the second piezoelectric/electrostrictive oscillator 203in such a way that it circumferentially extends along theinner-circumferential surface of the recess 207.

Further, on the bottom of the first U-shaped recess 207, there is formeda second bottom plate portion 208 and, in the second bottom plateportion 208, as illustrated in FIG. 12A, there are formed a plurality ofsecond U-shaped recesses 209 at the central part and in the neighborhoodthereof.

Further, in the bottom of the second U-shaped recess 209, there isformed a third bottom plate portion 210. On the underside of the thirdbottom plate portion 210, there is fixedly provided the above-describedpiezoelectric/electrostrictive oscillator 202. Incidentally, the firstpiezoelectric/electrostrictive oscillator 202 is in the form of anannulus and has a maximum diameter substantially equal to the diameterof the third bottom plate portion 210. Also, since the firstpiezoelectric/electrostrictive oscillator 202 has formed at its centralpart a hole, and, from this hole, the third bottom plate portion 210 isexposed.

The space which is surrounded by the circumferential wall portion 206 onthe first bottom plate portion 205 forms a solution accommodation largespace 211. Also, the space which is surrounded by the secondpiezoelectric/electrostrictive oscillator 203 on the second bottom plateportion 208 forms a solution accommodation middle space 212. Further,the space which is within the second U-shaped recess 209 on the thirdbottom plate portion 210 forms a solution accommodation small space 213.

Incidentally, the diameter of the first bottom plate portion 205 in thereaction cell 200 is preferably set to be at a value falling within arange of from several mm to several tens of cm. Also, the diameter ofthe second bottom plate portion 208 is preferably set to be at a valuefalling within a range of from several tens of μm to several mm.Further, the diameter of the third bottom plate portion 210 ispreferably set to be at a value falling within a range of from severalμm to several mm.

In the reaction cell 200 according to this embodiment, the thickness ofthe third bottom plate portion 210 is set to have a small thickness soas to permit a light to pass therethrough. And, since the firstpiezoelectric/electrostrictive oscillator 202 does not exist at thecentral part of the third bottom plate portion 210, it is possible todetect the status of solution within the second U-shaped recess 209 bymeasuring the optical transmittance through the third bottom plateportion 210.

The reaction cell 200 according to this embodiment also enables thereaction of the solution to be performed in a state where the solutionis accommodated within only the solution accommodation small space 213alone, or in a state where the solution is accommodated within thesolution accommodation middle space 212, or in a state where thesolution is accommodated within the solution accommodation large space211.

By driving the first piezoelectric/electrostrictive oscillator 202, theoscillation which has occurred in the piezoelectric/electrostrictiveoscillator 202 can be transmitted to the solution within the solutionaccommodation small space 213 as the deflection oscillation of the thirdbottom plate portion 210. Also, by driving the secondpiezoelectric/electrostrictive oscillator 203, the oscillation can betransmitted to the solution within the solution accommodation middlespace 212. Further, by driving the third piezoelectric/electrostrictiveoscillator 204, the oscillation can be transmitted to the solutionwithin the solution accommodation large middle space 211. As a result, aprescribed reaction of solution can be promoted within the reaction cell200.

Incidentally, in the reaction cell 200, as well, according to thisembodiment, the first, second and third piezoelectric/electrostrictiveoscillators 202, 203, and 204 are each connected to a drive controlcircuit via a wiring (not illustrated) so that the number ofoscillations and the oscillation length of time and so forth maysuitably be controlled.

In this embodiment, as in the case of the above-described eleventhembodiment, in the reaction cell 200, each of the first to thirdpiezoelectric/electrostrictive oscillators 202, 203, and 204 is soarranged that it can detect the changes in the specific gravity andviscosity that follow the change in the status of reaction of thesolution within the solution accommodation small space 213, solutionaccommodation middle space 212, or solution accommodation large space211 that is located close to or directly contacts with one of theoscillators. Concretely, by detecting the electric constant followingthe oscillation of each piezoelectric/electrostrictive oscillator, thespecific gravity and viscosity of the solution can be determined.

Thirteenth Embodiment

A thirteenth embodiment of the present invention will be described withreference to FIGS. 13A and 13B.

A reaction cell 300 according to this embodiment comprises a vessel-likecell main body 301 and a plurality of firstpiezoelectric/electrostrictive oscillators 302 provided on the underside(outside surface) of the cell main body 301, and secondpiezoelectric/electrostrictive oscillators 303 provided on the underside(outside surface) of the bottom portion of the cell main body at aposition other than that where the first piezoelectric/electrostrictiveoscillators have been formed.

The cell main body 301 is constructed of a first circular bottom plateportion 305, the thickness of which is great and when viewed from above,is circular and a circumferential wall portion 306 rises from andsurrounds the circumferential edge of the first bottom plate portion305, the both portions 305 and 306 being integrally formed using, forexample, zirconium ceramics.

In the first bottom plate portion 305, there are formed in theneighborhood of its central part a plurality of U-shaped recesses 307.In the relatively thin bottom plate 310 of each U-shaped recess 307there are formed a plurality of second U-shaped recesses 309. On thecentral part of the underside of a thin bottom plate 308 of each secondU-shaped recess 309 there is disposed and adhered thepiezoelectric/electrostrictive oscillator 302. Thepiezoelectric/electrostrictive oscillator 302 is circular and has adiameter substantially equal to the diameter of the bottom plate 310.The reaction cell 300 having such structure has a solution accommodationsmall space 313 within the second U-shaped recess 309, a solutionaccommodation middle space 312 within the U-shaped recess 307, and asolution accommodation large space 311 which is surrounded by thecircumferential wall portion 306 on the bottom plate 305. Further, inthe first bottom plate portion 305, there are formed at the central partof it and in the neighborhood of the central part which is other thanthe portions where the U-shaped recesses 307 are disposed a plurality ofU-shaped recesses 317. This U-shaped recess 317 is circular when viewedfrom above it and, on the underside of a thin bottom plate 320 at thatbottom surface, there are disposed and adhered thepiezoelectric/electrostrictive oscillator 303.

Incidentally, the diameter of the first bottom plate portion 305 in thereaction cell 300 is preferably set to be at a value falling within arange of from several mm to several tens of cm. Also, the diameter ofthe relatively thin bottom plate 310 at the second bottom plate portionis preferably set to be at a value falling within a range of fromseveral tens of μm to several mm. Further, the diameter of the thinbottom plate 308 at the third bottom plate portion is preferably set tobe at a value falling within a range of from several μm to several mm.

In the reaction cell 300 according to this embodiment, the secondpiezoelectric/electrostrictive oscillator 303 which has been optimallydesigned for movement and agitation of the solution within the solutionaccommodation large space 311 is formed whereby, by driving thepiezoelectric/electrostrictive oscillator, it is possible to freelyagitate the solution in the entire large cell including the smallercells. Incidentally, the configuration of the U-shaped recess 317 on thebottom plate of which there is formed the secondpiezoelectric/electrostrictive oscillator 303 is not limited inparticular but can be made into one that is suitable for moving andagitating the solution within the solution accommodation large space311. However, to efficiently transmit the oscillation of the secondpiezoelectric/electrostrictive oscillator 303 to the solution, thatconfiguration preferably is in the form of a U-shaped recess whichenables using the deflection oscillation of the thin bottom plate 320.

In the reaction cell 300 according to this embodiment, it is preferableto cause the reaction of the solution to be performed in a state wherethe solution is accommodated within every one of the solutionaccommodation small space 313, solution accommodation middle space 312,and solution accommodation large space 311.

Incidentally, in the reaction cell 300 according to this embodiment, thefirst and second piezoelectric/electrostrictive oscillators 302 and 303are each connected to a drive control circuit via a wiring (notillustrated) so that the number of oscillations and the oscillationlength of time and so forth may suitably be controlled.

Also, in the reaction cell 300, each of the first and secondpiezoelectric/electrostrictive oscillators 302 and 303 is so arrangedthat it can detect the change in the specific gravity and viscosity thatfollows the change in the status of reaction of the solution within thesolution accommodation small space 313, solution accommodation middlespace 312, or solution accommodation large space 311, which is locatedclose to or it directly contacts with one of the oscillators.Concretely, by detecting the electric constant following the oscillationof each piezoelectric/electrostrictive oscillator, the gravity and theviscosity of the solution can be determined. Incidentally, in the caseof the reaction cell 300, since the secondpiezoelectric/electrostrictive oscillator 303 does not exist inside thereaction cell, when the oscillator 303 is other than when it acts on themovement and agitation of the solution, it can be exclusively used formeasuring the specific gravity and viscosity. For this reason, finermonitoring becomes possible.

Fourteenth Embodiment

A fourteenth embodiment of the present invention will be described withreference to FIGS. 14A and 14B.

The structure of a reaction cell 400 according to this embodiment isthat a pair of first U-shaped recesses 107 are further added to thefirst bottom plate portion 105 in the reaction cell 100 according to theabove-described eleventh embodiment. Other constructions are the same asthose in the reaction cell 100 according to the eleventh embodiment andtherefore they are denoted by the same reference numerals and theirexplanation will be omitted.

Such reaction cell 400 is the one that is provided with four groups A,B, C, and D each of which includes a plurality of solution accommodationsmall spaces 113 such as those illustrated in FIG. 14A. The reactioncell 400 is advantageous when those groups A, B, C, and D correspondingto the solution accommodation small spaces 113 are used for immobilizingthe captures having adsorption specificity such as immune bodies ofdifferent kinds. Incidentally, the method of using the reaction cell 400will later be described.

EXAMPLES

Next, Examples that use the reaction cells according to the presentinvention will be described.

First of all, a reaction cell according to the present invention whichis provided with a piezoelectric/electrostrictive oscillator and anordinary cell which is not provided with apiezoelectric/electrostrictive oscillator were prepared. It is to benoted that each of the reaction cell and ordinary cell is provided withmore than 15 solution accommodation spaces.

A 30% (w/v) aqueous solution of sucrose was poured into each of 15solution accommodation spaces of each of the reaction cell and ordinarycell and was pre-incubated at a temperature of 37° C.

After each cell had been pre-incubated for 10 minutes, a fixed quantityof sucrose hydrolase was added, at intervals of 2 seconds, to the cellsone lot per cell.

Next, after the enzyme was added, at various lengths of time from 1 to60 minutes, the reaction solution was sampled from each cell and theglucose was determined (colorimetry determined with a spectrophotometer,such as an F-kit made by Berlinger/Manheim Company). The results areshown in a graph depicted in FIG. 16 along the abscissa axis of whichthe reaction length of time is plotted and along the ordinate axis ofwhich the yield (the quantity of glucose produced/the quantity ofsucrose added (W/W)) is plotted.

As illustrated in FIG. 16, in the reaction cell (oscillation cell)according to the present invention which is provided with thepiezoelectric/electrostrictive oscillator, the reaction properlyproceeded up to around a theoretical value, whereas, in the ordinarycell, the speed at which the reaction proceeded was low and, inaddition, data variance was also wide.

[Method of Manufacturing a Reaction Cell]

Next, various kinds of manufacturing methods according to the presentinvention will briefly be described.

(Method of Manufacturing Using Zirconia)

First, green sheets of zirconia were suitably laminated and were formedinto a configuration as a cell main body. Thereafter, the green sheetlaminate was sintered and produced into the cell main body.

Next, on the reverse surface of the bottom plate portion of the cellmain body, a lower electrode, piezoelectric/electrostrictive member, andupper electrode were sequentially formed by printing and sinteringtechniques. By doing so, it is possible to produce a reaction cell.

(Method of Manufacturing by Cutting Working)

Alumina having optical transmissivity which was sintered in bulk wascutting worked and was worked into a configuration as a cell main body.Thereafter, a piezoelectric/electrostrictive oscillator was fabricated.In the method of fabricating a piezoelectric/electrostrictiveoscillator, a lower electrode, piezoelectric/electrostrictive layer, andupper electrode were sequentially printed to a prescribed position ofthe cell main body, after which sintering was performed to fabricate areaction cell.

(Method of Manufacturing by Pasting a Transparent Plate)

A cell main body is formed by laminating ceramic green sheets so thatthe portion where a solution is accommodated may become a through-hole.Thereafter, the laminate consisting of the ceramic green sheets issintered. After that, a plate consisting of a transparent glass orsynthetic resin is adhered to the underside of the sintered body byadhesive agent, or thermal diffusion, or thermal bond (in a case wherethe synthetic resin is thermoplastic resin) to thereby fabricate a cellmain body. Further, a piezoelectric/electrostrictive oscillator isadhered onto a suitable position of the cell main body by using anadhesive agent to thereby fabricate a reaction cell.

(Method of Manufacturing by Using Etched Glass)

Transparent glass is etching worked and a U-shaped recess is therebyformed. After that, a piezoelectric/electrostrictive oscillator isadhered onto the resulting structure by using an adhesive agent tothereby fabricate a reaction cell.

(Method of Manufacturing by Using a Transparent Synthetic Resin)

Transparent synthetic resin material is poured into a die to therebyform a cell main body, and a piezoelectric/electrostrictive oscillatoris adhered onto a suitable position by using an adhesive agent tothereby form a reaction cell.

Although various kinds of the manufacturing methods for fabricating areaction cell have been described as above, in a case where, forexample, a capture having adsorption specificity needs to be adhered towithin the reaction cell, as one method the capture may be immobilizedto the reaction cell which has been manufactured with theabove-described method. However, as an alternative to that, atransparent glass or transparent synthetic resin having immobilizedthereto beforehand the capture may be adhered to a wall portion of thecell main body.

Incidentally, when fabricating a piezoelectric/electrostrictiveoscillator, the process step wherein pastes containing thereinrespective raw materials of a lower electrode,piezoelectric/electrostrictive element layer, and upper electrode areprinted onto the cell main body by screen printing is repeatedlyexecuted for every one of the lower electrode,piezoelectric/electrostrictive element layer, and upper electrode, tothereby form a laminate. Then, the laminate needs only to be sintered.Or, a respective one of the pastes may be sintered for every printing,or both techniques may be combined together. Here, as the method ofsupplying the pastes containing therein the raw materials onto theceramics, in a case where supplying them to the underside of the bottomplate portion, they can be supplied by screen printing. However, in acase where supplying them to the circumferential wall portion, athrough-hole printing technique may be used, or they may be supplied bydipping into the solution containing therein the respective rawmaterials the cell main body having masked its portions where thepiezoelectric/electrostrictive oscillator is not formed. Also,especially the upper electrode is not limited to being formed byprinting, dipping, and sintering but may be formed by using a thin filmforming technique such as a sputtering technique, a depositiontechnique, etc.

[Method of Using a Reaction Cell]

The method of using the reaction cell 400 according to theabove-described thirteenth embodiment will be described next withreference to FIG. 15.

(First Method of Using)

FIG. 15 shows that groups A, B, C, and D each include 9 solutionaccommodation small spaces 113 and reference letters a, b, c, d, e, f,g, h, and i sequentially represent 8 small spaces and 1 center space,respectively, clockwise as shown in FIG. 15. Into each of the spaces ato h, there is poured a different diluted stage of enzyme solution, theactivity of which is unknown. Here, the space i is left blank. Afterthat, the first piezoelectric/electrostrictive oscillator 102, which isprovided on the underside of the space having the solution accommodatedtherein, is driven for a prescribed length of time to thereby transmit aprescribed strength of oscillation to the solution within each space.After the passage of a prescribed reaction length of time, the status ofthe solution is detected by performing a colorimetry analysis of thesolution in each space or by measuring the viscosity of the solution.Incidentally, colorimetry can be performed, for example, by radiating alight from a position above the reaction cell 400 toward a positionbelow it and by measuring the optical transmittance of a light, passingthrough the third bottom plate portion 110, on the side of the undersideof the reaction cell 400. Also, the measurement of the viscosity may beperformed simply by detecting the change in the electric constantfollowing the oscillation of the first piezoelectric/electrostrictiveoscillator 102 and by determining the viscosity of the solution. Bydetecting the status of the solution in that way, it is possible tocalculate the activity (U) of the enzyme.

(Second Method of Using)

Into each of the spaces a to h illustrated in FIG. 15, there is poured adifferent diluted stage of enzyme solution, the activity of which isunknown. Here, the space i is made blank. Next, by driving the firstpiezoelectric/electrostrictive oscillator 102 and by, after the passageof a prescribed length of time, (even when it is unclear what kind ofreaction has been proceeding in that state) putting a mixed solution ofenzyme substrate that is predicted into the solution accommodationmiddle space 112, the resulting solution is caused to react. At thistime, the second piezoelectric/electrostrictive oscillator 103 whichsurrounds solution accommodation middle space 112 is driven and thesolution is agitated, thereby the reaction is promoted.

By performing colorimetry or measuring the viscosity of the solution inthe same way as in the above-described method, it is determined whichsubstrate has reacted. By doing so, the function of the enzyme and thespecificity of the substrate can be determined.

(Third Method of Using)

Into the groups A, B, C, and D each having the solution accommodationsmall spaces illustrated in FIG. 15, there are immobilized,respectively, the captures having adsorption specificity such as fordifferent kinds of antibodies sampled from respective organs (e.g.liver, spleen, blood, and large intestine) of a living organism. Intothe solution accommodation middle spaces 112 of the respective groups,there are added the samples taken away from the respective organs. Atthis time, the first and second piezoelectric/electrostrictiveoscillators 102, 103 are driven. By this driving, the solution withinthe respective solution accommodation middle spaces 112 is agitated,thereby a biochemical reaction is promoted.

After the passage of a prescribed reaction length of time, the degree ofprogress of the reaction in each of the groups A, B, C, and D isdetermined by performing pattern recognition, and, by this, it ispossible to determine whether the relevant organ has an abnormality.That pattern recognition can be performed, because the third bottomplate portion 110 has optical transmissivity, from the side of theunderside of the reaction cell 400.

As is apparent from the foregoing explanation, in the present invention,by setting the length of time during which thepiezoelectric/electrostrictive oscillator oscillates, the intervals atwhich the oscillation is made, etc., it is possible to control thedegree of the progress of the reaction of the solution and the reactionlength of time and so forth. For this reason, it is possible to performsufficient, uniform agitation with no contamination occurring betweenthe cells and within a very small space. Since the configuration of thepiezoelectric/electrostrictive oscillator can be freely designed,optical sensing is possible, i.e. it is possible to optically grasp thestatus of the solution.

According to the present invention, when the chemical reaction of thesolution proceeds and for example the specific gravity, viscosity, etc.of the solution has varied, it is possible to detect the change in theelectric constant following the oscillation of thepiezoelectric/electrostrictive oscillator and, thereby, to detect thestatus of the reaction, and, further, the degree of progress of thereaction and the status of the reaction. Therefore, it is possible toperform optimum oscillation while sensing the status of the specificgravity, viscosity, etc.

Further, according to the present invention, it is possible to performthe control of the agitation, the control of the reaction, the detectionof the status, etc. for every cell by controlling the operation of thepiezoelectric/electrostrictive oscillator provided for the relevantcell. Also, it is possible for the piezoelectric/electrostrictiveoscillator to transmit its oscillation directly to the solution and itis possible to independently control the oscillation for every cell.

Also, by driving the piezoelectric/electrostrictive oscillator providedfor the cell including a plurality of cells, it is possible to evenlyagitate the solution in these cells as a whole. In addition, regardingthe respective individual cells that are included, they can be agitationcontrolled by using the relevant piezoelectric/electrostrictiveoscillators.

Further, it is possible to detect the change in the electric constantfollowing the oscillation of the piezoelectric/electrostrictiveoscillator, and, thereby, to detect the specific gravity, viscosity,etc. of the solution, and, thereby, to detect the status of the reactionof the solution.

The contents of Japanese Patent Application No. 2002-56041 (filed onMar. 1, 2002) are incorporated herein by reference in its entirety.

Although the invention has been described above by reference to certainembodiments of the invention, the invention is not limited to theembodiments described above. Modifications and variations of theembodiments described above will occur to those skilled in the art, inlight of the above teachings.

For instance, although in the above-described eleventh to fourteenthembodiments the spaces which are formed in the reaction cell have beenprovided in three stages of the solution accommodation large space,solution accommodation middle space, and solution accommodation smallspace, the spaces may also be constructed in a larger number of stages,i.e. in the way the reaction cell has a solution accommodation spacewherein smaller U-shaped recesses are formed in the bottoms of thesolution accommodation small spaces. Namely, within a large solutionaccommodation space, solution accommodation spaces the sizes of whichare sequentially reduced may be formed stepwise so that they may form apiece of nesting.

Also, in the reaction cell of the present invention, the number of thesolution accommodation spaces formed in the interior thereof cansuitably be changed according to the solution used and the purpose ofthe analysis. For example, they may be disposed in the form of a matrix.

1. A reaction cell, comprising: a cell having a main body including acircumferential wall portion and a bottom portion forming a space toaccommodate a solution, said main body comprising at least one ofceramic and glass; and a piezoelectric/electrostrictive oscillatorformed integrally with at least one surface of the circumferential wallportion, and at least a part of the bottom portion so as to agitate thesolution, wherein an amplitude (Δd) of thepiezoelectric/electrostrictive oscillator and a length (d) of the cellin a vibration direction thereof satisfy the following inequality:0.000001<Δd/d<0.01.
 2. The reaction cell of claim 1, wherein thepiezoelectric/electrostrictive oscillator further comprises electronicmeans for detection of a change in the electric constant of theoscillator.
 3. The reaction cell of claim 1, wherein the reaction cellcomprises a plurality of the cells.
 4. The reaction cell of claim 1,wherein the circumferential wall portion and the bottom portion comprisezirconia and are integrally sintered.
 5. The reaction cell of claim 1,wherein the circumferential wall portion and the bottom portion compriseoptically transmissive ceramics and are integrally sintered.
 6. Thereaction cell of claim 1, wherein the circumferential wall portioncomprises ceramics and the bottom portion comprises transparent glass.7. The reaction cell of claim 1, wherein the circumferential wallportion comprises ceramics and the bottom portion comprises atransparent synthetic resin.
 8. The reaction cell of claim 1, whereinthe circumferential wall portion and the bottom portion comprise atransparent glass or a transparent synthetic resin and thepiezoelectric/electrostrictive oscillator is formed integrally with thecircumferential wall portion or the bottom portion.
 9. The reaction cellof claim 1, wherein the bottom portion of the cell further comprises oneor more first recess portions which accommodate the solution.
 10. Areaction cell comprising: a cell having a main body including acircumferential wall portion and a bottom portion forming a space toaccommodate a solution; and a piezoelectric/electrostrictive oscillatorformed integrally with at least one of a surface of the circumferentialwall portion and a part of the bottom portion so as to agitate thesolution, wherein an amplitude (Δd) of thepiezoelectric/electrostrictive oscillator and a length (d) of the cellin a vibration direction thereof satisfy an inequality of0.000001<Δd/d<0.01.
 11. A method of using a reaction cell, comprising:accommodating a solution in a reaction cell in which a plurality ofpiezoelectric/electrostrictive oscillators are disposed along one of acircumferential wall surface of the reaction cell and a bottom surfaceof the reaction cell; and oscillating the piezoelectric/electrostrictiveoscillators sequentially in a circumferential direction of the reactioncell, wherein an amplitude (Δd) of at least one of thepiezoelectric/electrostrictive oscillators and a length (d) of the cellin a vibration direction thereof satisfy an inequality of0.000001<Δd/d<0.01.
 12. A method of using a reaction cell, comprising:accommodating a solution in a first reaction cell in which a pluralityof piezoelectric/electrostrictive oscillators are fixed directly to oneof a circumferential wall surface of the first reaction cell and abottom surface of the first reaction cell; and oscillating thepiezoelectric/electrostrictive oscillators with an amplitude and atiming that are independently controlled, wherein at least a portion ofthe piezoelectric/electrostrictive oscillator has no opticaltransmissivity, wherein an amplitude (Δd) of at least one of thepiezoelectric/electrostrictive oscillators and a length (d) of the cellin a vibration direction thereof satisfy an inequality of0.000001<Δd/d<0.01.